Experimental Data Analysis Answer Key · Statistical Analysis of Methods to Repair Cracked Steel Activity—Experimental Data Analysis Answer Key 4 The analysis of Data Set 3 shows

Statistical Analysis of Methods to Repair Cracked Steel Activity—Experimental Data Analysis Answer Key 1

Experimental Data Analysis Answer Key

Department of Civil and Environmental Engineering, University of Massachusetts, MA, USA

Data Set 1

Statistics Unpatched Specimens

Patched Specimens

Patching Configuration

Sample mean: x 173,418.267 276,733.167

Sample std dev: Sx = 31,917.338 85,681.856

C. variation (%): Cv = 18.405 30.962

Minimum Min = 114,189 159,747

First quartile: Q1 = 154,586 212,374

Median: Q2 = 178,796 256,072

Third quartile: Q3 = 198,140 360,752

Maximum Max = 212,164 457,370

10% trim mean: %10x

176,636.535 270,596.357

Efficiencies: ER = 159.576 % EM = 143.22 % unstressed/one-side patches

80 MPa, 15 Hz

The analysis of Data Set 1 shows that the CFRP patching arrangement used increased the mean fatigue

life (MFL) of cracked steel specimens about 1.6 times, but the variability of this extended MFL was about

three times greater than the variability of the MFL of the unpatched specimens. In the five-number

Figure A. The first repair method

proposed by the University of

Massachusetts is expected to increase

the mean fatigue life of cracked steel

specimens about 1.6 times and be

effective about 75% of the time.

This box-and-whisker plot compares the

fatigue life data of patched and

unpatched specimens tested at the

University of Massachusetts.


summary graph for this data set (Figure A), it can be seen that about 75% of the patched specimens

performed better than the unpatched specimens; in 25% of the patched specimens the patching was

ineffective. Reading the medians of the specimens tested, the relative median efficiency is about 1.4,

similar to the MFL ratio. In summary, this method is expected to extend the MFL of cracked steel about

1.6 times in only 75% of the repairs.

Data Set 2


Patched Specimens


Sample mean: x 346,922.125 434,118.313

Sample std dev: Sx = 33,659.442 88,707.717

C. variation (%): Cv = 9.702 20.434

Minimum Min = 283,173 274,551

First quartile: Q1 = 326,142.5 377,013.5

Median: Q2 = 347,281 434,046.5

Third quartile: Q3 = 368,395 483,028

Maximum Max = 410,671 617,712

10% trim mean: %10x

347,432.75 431,906


80 MPa, 15 Hz

Figure B. The second repair method

proposed by the University of

Massachusetts is expected to increase

the mean fatigue life of cracked steel


effective about 50% of the time.




University of Massachusetts.



life (MFL) of cracked steel specimens on average by 1.25 times, with a variability for this extended MFL

about 2.6 times greater than the variability of the MFL of the unpatched specimens. In the five-number

summary graph for this data set (Figure B), it can be seen that about 50% of the patched specimens

performed better than the unpatched specimens; in practically half of the patched specimens the patching

was ineffective. In both, patched and unpatched specimens, the corresponding means and medians were

practically identical, no significant difference was found between median fatigue life ratio (patched to

unpatched) and the MFL ratio. In summary, this method is expected to extend the mean fatigue life of

cracked steel about 1.25 times in only 50% of the repairs.

School of Civil Engineering, Southwest Jiaotong University. China

Institute for Rehabilitation of Buildings and Structures, University of Braunschweig, Germany

Data Set 3


Patched Specimens


Sample mean: x 165,333.333 226,000

Sample std dev: Sx = 14,105.662 16,236.883

C. variation (%): Cv = 8.53 7.18

Minimum Min = 136,000 198,000

First quartile: Q1 = 160,000 216,500

Median: Q2 = 166,500 223,500

Third quartile: Q3 = 173,000 239,000

Maximum Max = 189,000 255,000

10% trim mean: %10x

165,900 225,900


117 MPa, 25 Hz



life (MFL) of cracked steel specimens on average by 1.4 times, with a variability practically the same as

the variability of the MFL of the unpatched specimens. In the graph of the five-number summary for this

data set (Figure C), it can be seen that all the patched specimens (100%) performed better than the

unpatched specimens. Reading the medians of the specimens tested, the relative median efficiency

increased about 1.34 times, very close to the MFL ratio. In summary, this method is expected to extend

the mean fatigue life of cracked steel about 1.4 times.

Data Set 4


Patched Specimens


Sample mean: x 165,333.333 556, 500

Sample std dev: Sx = 14,105.662 47,038.669

C. variation (%): Cv = 8.53 8.45

Minimum Min = 136,000 474,000

First quartile: Q1 = 160,000 525,000

Median: Q2 = 166,500 557,500

Third quartile: Q3 = 173,000 587,500

Maximum Max = 189,000 639,000

10% Trim mean: %10x

165,900 556,500

Efficiencies: ER = 365.593 % EM = 334.835 % stressed patches @ 1200 MPa

117 MPa, 25 Hz

Figure C. The first repair method

proposed by the Universities of Jiatong

and Braunschweig is expected to

increase the mean fatigue life of cracked

steel specimens about 1.4 times and be

effective 100% of the time.




Universities of Jiatong and

Braunschweig.



life (MFL) of cracked steel specimens on average by 3.7 times, with a variability very similar to the

variability of the MFL of the unpatched specimens. In the graph of the five-number summary for this data

set (Figure D), it can be seen that all the patched specimens (100%) performed better than the unpatched

specimens. Reading the medians of the specimens tested, the relative median efficiency increased about

3.35 times, close to the MFL ratio. In summary, this method is expected to extend the mean fatigue life of

cracked steel about 3.7 times.

Figure D. The second repair method

proposed by the Universities of Jiatong

and Braunschweig is expected to

increase the mean fatigue life of cracked

steel specimens about 3.4 times and be




unpatched specimens, tested at the

Universities of Jiatong and

Braunschweig.


School of Naval Architecture and Marine Engineering, National Technical University of Athens, Greece

Data Set 5


Patched Specimens


Sample mean: x 40,143 63,889

Sample std dev: Sx = 1,422.221 9,116.042

C. variation (%): Cv = 3.543 14.269

Minimum Min = 38,035 47,053

First quartile: Q1 = 39,065 59,306

Median: Q2 = 39,873.5 61,536

Third Quartile: Q3 = 41,375 69,789

Maximum Max = 42,251 80,963

10% trim mean: %10x

40,143 63,869.167


100 MPa, 2 Hz


life (MFL) of cracked steel specimens on average by 1.6 times, but the variability of this extended MFL is

about 6.4 times the variability of the MFL of the unpatched specimens. In the graph of the five-number

summary for this data set (Figure E), it can be seen that all the patched specimens (100%) performed

better than the unpatched specimens. Reading the medians of the specimens tested, the relative median

Figure E. The repair method proposed

by the National Technical University of

Athens is expected to increase the mean

fatigue life of cracked steel specimens

about 1.6 times and be effective 100% of

the time.

The box-and-whisker plot compares the



National Technical University of

Athens.


efficiency increased about 1.54 times, very close to the MFL ratio. In summary, this method is expected to

extend the mean fatigue life of cracked steel about 1.6 times.

Department of Civil Engineering, Technical University of Denmark, Brovej, Denmark

Data Set 6


Patched Specimens


Sample mean: x 470,000 1,433,789.929

Sample std dev: Sx = 8,769.783 181,903.011

C. variation (%): Cv = 1.866 12.687

Minimum Min = 454,000 1,157,369

First quartile: Q1 = 465,000 1,328,369

Median: Q2 = 471,000 1,394,184.5

Third quartile: Q3 = 477,500 1,527,369

Maximum Max = 481,000 1,767,369

10% trim mean: %10x

470,500 1,429,026.75

Efficiencies: ER = 305.062 % EM = 296.005 % unstressed/two-sides patches

97.5 MPa, 13.5 Hz


life (MFL) of cracked steel specimens on average by 3 times, but the variability of this extended MFL is

Figure F. The first repair method

proposed by the Technical University of

Denmark is expected to increase the

mean fatigue life of cracked steel

specimens about 3 times and be effective

100% of the time.




Technical University of Denmark.


about 21 times the variability of the MFL of the unpatched specimens. However, in the five-number

summary graph for this data set (Figure F), it can be seen that all the patched specimens (100%)

performed much better than the unpatched specimens; the lowest MFL of the patched set is 2.4 times the

maximum MFL of the unpatched set. Reading the medians of the specimens tested, the relative median

efficiency increased about 2.96 times, very close the MFL ratio. In summary, this method is expected to

extend the mean fatigue life of cracked steel about 3 times.

Data Set 7


Patched Specimens

Patching Configuration (Two-sides patching)

Sample mean: x 470,000 8,230,000

Sample std dev: Sx = 8,769.783 2,866,386.092

C. variation (%): Cv = 1.866 34.829

Minimum Min = 454,000 3,780,000

First quartile: Q1 = 465,000 6,730,000

Median: Q2 = 471,000 8,275,000

Third quartile: Q3 = 477,500 8,560,000

Maximum Max = 481,000 15,980,000

10% trim mean: %10x

470,500 7,955,000

Efficiencies: ER = 1,751.064 % EM = 1,756.900 % stressed patches @ 13.5 KN

97.5 MPa, 13.5 Hz

Figure G. The second repair method

proposed by the Technical University of

Denmark is expected to increase the

mean fatigue life of cracked steel






Technical University of Denmark.



life (MFL) of cracked steel specimens on average by 17.5 times, but the variability of this extended MFL

is huge compared with the variability of the MFL of the unpatched elements: 327 times! Analyzing the

coefficients of variation, the CV for the patched set is about 19 times greater than the CV for the

unpatched set, which indicates that even though this patching method increases the MFL considerably, the

variability increases proportionally. A possible explanation of the small variability of the MFL of the

unpatched elements could be the use of a very standard quality of the specimens in the experiment. The

high variability of the patched elements could be the consequence of using a non-standard patching

method, and some steps in this process may not be completely under control.

In the five-number summary graph for this data set (Figure G), two outliers in the patched box-and-

whisker plot can be observed; the high MFL value that patched specimen achieved is notable, however

the 10% trimmed mean of this data set is about the same as its MFL. Reading the medians of the

specimens tested, the relative median efficiency is about 17.6 times, practically equal to the MFL ratio. In

summary, this method is expected to extend the mean fatigue life of cracked steel about 17.5 times.


Department of Civil Engineering, Monash University, Clayton, Victoria, Australia

Data Set 8


Patched Specimens


Sample mean: x 241,641.5 373,466.25

Sample std dev: Sx = 1,891.644 55,032.453

C. variation (%): Cv = 0.783 14.736

Minimum Min = 238,333 298,757

First quartile: Q1 = 240,871.5 342,753.5

Median: Q2 = 241,614.5 350,812

Third quartile: Q3 = 242,749 418,245

Maximum Max = 244,950 478,351

10% trim mean: %10x

241,641.5 370,448.7

Efficiencies: ER = 154.554 % EM = 145.195 % unstressed/one side patches

135 MPa, 30 Hz



big compared with the variability of the MFL of the unpatched elements: 29 times. Analyzing the


unpatched set, the increase in variability is not proportional to the increase in MFL.

Figure H. The first repair method

proposed by Monash University is

expected to increase the mean fatigue

life of cracked steel specimens about 1.5

times and be effective 100% of the time.



unpatched specimens tested at Monash

University.


However, in the five-number summary graph for this data set (Figure H), it can be seen that all the

patched specimens (100%) performed better than the unpatched specimens. Reading the medians of the

specimens tested, the relative median efficiency is about 1.45 times, close to the MFL ratio. In summary,

this method is expected to extend the mean fatigue life of cracked steel about 1.6 times.

Data Set 9


Patched Specimens


Sample mean: x 241,641.5 1,278,717.583

Sample std dev: Sx = 1,891.644 412,781.576

C. variation (%): Cv = 0.783 32.281

Minimum Min = 238,333 542,353

First quartile: Q1 = 240,871.5 1,044,597.5

Median: Q2 = 241,614.5 1,293,238

Third quartile: Q3 = 242,749 1,561,380

Maximum Max = 244,950 1,920,000

10% trim mean: %10x

241,641.5 1,288,225.8

Efficiencies: ER = 529.180 % EM = 536.249 % unstressed/two sides patches

135 MPa, 30 Hz



huge compared with the variability of the MFL of the unpatched elements: 218 times! Analyzing the

Figure I. The second repair method

proposed by Monash University is

expected to increase the mean fatigue

life of cracked steel specimens about 5.3

times and be effective 100% of the time.



unpatched specimens tested at Monash

University.



unpatched set. In this case the variability in the MFL of the patched specimens is not proportional to the

increase of the MFL. Again, the differences in variability could be attributed to the steel specimens’

consistent quality and to factors that affect the patching process performance being not fully under

control.

However, in the five-number summary graph for this data set (Figure I), it can be seen that all the patched

specimens (100%) performed better than the unpatched specimens. Reading the medians of the specimens

tested, the relative median efficiency is about 5.35, practically equal to the MFL ratio. In summary, this

method is expected to extend the mean fatigue life of cracked steel about 5.3 times.


Department of Architecture, Built Environment and Construction Engineering, ABC Politecnico di Milano, Milan, Italy

Data Set 10


Patched Specimens

Patching Configuration (6mm notch)

Sample mean: x 196,714 435,110

Sample std dev: Sx = 9,604.418 142,035.132

C. variation (%): Cv = 4.883 32,644

Minimum Min = 181,171 58,400

First quartile: Q1 = 187,415 378,037

Median: Q2 = 196,714 444,563

Third quartile: Q3 = 204,627 512,000

Maximum Max = 213,690 616,695

10% trim mean: %10x

196,554.778 451,370.417


90 MPa, 18 Hz


life (MFL) of cracked steel specimens on average by 2.2 times, with a variability about 15 times greater

than the variability of the MFL of the unpatched specimens. Analyzing the coefficients of variation, the

Figure J. The first repair method

proposed by the ABC Politecnico di

Milano is expected to increase the mean


about 2.2 times and be effective

practically 100% of the time.

This box-and-wisker plot compares the


unpatched specimens tested at the ABC

Politecnico di Milano.


CV for the patched set is about 6.7 times greater than the CV for the unpatched set, an increase that could

be considered proportional to the change in the MFL.

In the five-number summary graph for this data set (Figure J), it can be seen that all the patched


tested, the relative median efficiency is about 2.26, practically equal to the MFL ratio. In summary, this

method is expected to extend the mean fatigue life of cracked steel about 2.2 times.

Data Set 11


Patched Specimens

Patching Configuration (15mm notch)

Sample mean: x 29,264 109,760

Sample std dev: Sx = 1,040.922 29,956.897

C. variation (%): Cv = 3.557 27.293

Minimum Min = 26,899 66,800


Median: Q2 = 29,294 107,405.5

Third quartile: Q3 = 29,693 129,331

Maximum Max = 30,961 172,000

10% trim mean: %10x

29,338.222 108,153.333


90 MPa, 18 Hz

Figure K. The second repair method

proposed by the ABC Politecnico di

Milano is expected to increase the mean


about 3.75 times and be effective 100%

of the time.

The box-and-whisker plot compares the


unpatched specimens tested at the ABC

Politecnico di Milano.



life (MFL) of cracked steel specimens on average by 3.75 times, with a variability about 29 times greater


CV for the patched set is about 7.7 times greater than the CV for the unpatched set, an increase that could

be considered proportional to the change in the MFL.

In the five-number summary graph for this data set (Figure K), it can be seen that all the patched


tested, the relative median efficiency is about 3.67, very close to the MFL ratio. In summary, this method

is expected to extend the mean fatigue life of cracked steel about 3.75 times.


Department of Civil Engineering, Cullen College of Engineering, University of Houston, TX, USA

Data Set 12


Patched Specimens


Sample mean: x 47,435 990,000

Sample std dev: Sx = 1,844.008 86,497.6656

C. variation (%): Cv = 3.887 8.737

Minimum Min = 44,265 840,000


Median: Q2 = 48,176.5 984,500

Third quartile: Q3 = 48,622 1,045,000

Maximum Max = 49,868 1,140,000

10% trim mean: %10x

47,496.417 990,000

Efficiencies: ER = 2,087.067 % EM = 2,043.527 % stressed patches @ 30 MPa

153 MPa, 10 Hz


life (MFL) of cracked steel specimens on average by 21 times, with a variability about 47 times greater


CV for the patched set is about 2.25 times greater than the CV for the unpatched set, an increase that is

Figure L. The repair method proposed

by the University of Houston is expected

to increase the mean fatigue life of

cracked steel specimens about 21 times

and be effective 100% of the time.




University of Houston.


very proportional to the change in the MFL, and this fact suggests that this patching process has under

control most the variables that could cause performance problems.

In the five-number summary graph for this data set (Figure L), it can be seen that all the patched

specimens (100%) performed a lot better than the unpatched specimens. Reading the medians of the

specimens tested, the relative median efficiency is about 20.4 times, practically equal to the MFL ratio. In

summary, this method is expected to extend the mean fatigue life of cracked steel about 21 times.

Relative Efficiencies Analysis As can be noticed from the above data, every laboratory setup has very different experimental conditions:

specimens’ cracking and patching configurations, stresses applied on specimens, frequency of the stress

applied, CFRP specifications and brand, epoxy adhesive used, preparation method used, and many more.

All the above mentioned factors make impossible a direct comparison of the experimental results. But in

every experimental setup it is possible to evaluate the relative efficiency of the method: the times the

mean fatigue life (MFL) was extended, and this is a good point of comparison.

The following table summarizes the relative efficiencies of every repair method analyzed:

CFRP Patching Relative Efficiencies Summary

Data Set Research Center Relative Efficiencies % (ER, EM)

1 Department of Civil and Environmental Engineering University of Massachusetts, MA, USA

159.576 143.220

2 Department of Civil and Environmental Engineering University of Massachusetts, MA, USA

125.134 124.984

3

School of Civil Engineering, Southwest Jiaotong University, China

Institute for Rehabilitation of Buildings and Structures, University of Braunschweig, Germany

136.694 134.234

4

School of Civil Engineering Southwest Jiaotong University, China

Institute for Rehabilitation of Buildings and Structures University of Braunschweig, Germany

336.593 334.835

5 School of Naval Architecture and Marine Engineering National Technical University of Athens, Greece

159.154 154.328

6 Department of Civil Engineering Technical University of Denmark, Brovej, Denmark

305.062 296.005

7 Department of Civil Engineering Technical University of Denmark, Brovej, Denmark

1,751.064 1,756.900

8 Department of Civil Engineering Monash University, Clayton, Victoria, Australia

154.554 145.195


9 Department of Civil Engineering Monash University, Clayton, Victoria, Australia

529.180 536.249

10 Department of Architecture Built Environment and Construction Engineering ABC Politecnico di Milano, Milan, Italy

221.189 225.995

11 Department of Architecture Built Environment and Construction Engineering ABC Politecnico di Milano, Milan, Italy

375.068 366.647

12 Department of Civil Engineering Cullen College of Engineering University of Houston, TX, USA

2,087.067 2,043.527

A graphical display of the above data (Figure M) makes it easy to identify the most efficient repair

methods. Two methods had an outstanding performance—the second method proposed by the University

of Denmark and the one proposed by the University of Houston. Both performances extend the MFL

about 20 times (17.5 and 21.5, respectively).

Figure M. CFRP Relative Efficiencies Graphical Comparison.

From the direct comparison of the relative efficiencies, it can be concluded that the best repair

methods proposed come from the University of Denmark and the University of Houston.


It is also notable that the best repair methods proposed were those using pre-stressed patches, as can be

easily seen in a Pareto Chart of the Relative Efficiencies (Figure N).

In conclusion, the best proposed cracked steel repair method was the CFRP-NiTiNb pre-stressed patches

developed in the Cullen College of Engineering at the University of Houston.

It is important to make students aware that in real life, additional constraints must be considered in order

to make a final choice and purchase: procedure cost, implementation time, implementation plan, quality

control, warranties, maintenance schedule, and emergency response time are just some of the important

factors to be considered. Be sure that students include mention of these constraints in their preliminary

report to the mayor and city council.

Figure N. CFRP Relative Efficiencies Pareto Chart. In this Pareto chart, it can be seen that the repair methods

using pre-stressed CFRP patches are among the first five most-efficient procedures.

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Experimental Data Analysis Answer Key · Statistical Analysis of Methods to Repair Cracked Steel Activity—Experimental Data Analysis Answer Key 4 The analysis of Data Set 3 shows